A-LevelFurther MathematicsRoots of polynomial equations9231/12 · May/June 2023 · Q28 Marks
The cubic equation x^3 + 4x^2 +6x+1 = 0 has roots α, β, γ.
- (a)Find the value of α^2 + β^2 + γ^2.[2]
- (b)Use standard results from the list of formulae (MF19) to show that ∑(from r=1 to n) ((α+r)^2 + (β+r)^2 + (γ+r)^2) = n(n^2 +an+b), where a and b are constants to be determined.[6]
Mark scheme
Marking points from the official mark scheme (May/June 2023). The mark or mark type is shown in brackets.
- M1 Uses formula for sum of squares.
- A1 4
- B1 Expands.
- M1 A1 Collects like terms and uses α+β+γ = −4 and their result from part (a).
- M1 Applies formulae from MF19.
- M1 A1 Simplifies.
Write your answer and get it marked
On Oracle Prep you can write or photograph your own answer and have it marked by AI against this mark scheme, with feedback on what you missed.
Sign up free →